I have been lurking for a while and have only just recently started posting.
To be fair 'despair' I have winced at some of the statements you make as fact.
You should research your subject matter better as others have said or just keep schtum and let others who know better respond.

despair wrote:Having had to cut through 4inch diameter roots that have spread 10ft across my garden

That one has quite probably found a defective drain!

despair wrote:Even 6ft away the roots are 2inches in diameter

Roots are adventitious and will go wherever they go to find moisture and nutrients, with the amount of compost and water you claim to be putting on the area I'm sure your neighbour and his trees are delighted...............but of course with your slabs on edge remedy (was it 18" or 2' - you claim both?) there should be no roots!